References: 

• 1. B. Ebenman, R. Law and C. Borrvall, Community viability analysis: The response of ecological
• 2. M. E. Soulé and J. Terborgh, Protecting nature at regional and continental scales: A conservation biology program for the new millennium, BioScience, 49 (1999), 809–817.
• 3. O. J. Schmitz, P. A. Hamback and A. P. Beckerman, Trophic cascades in terrestrial systems: A review of the effects of carnivore removal on plants, Am. Nat., 155 (2000), 141–153.
• 4. M. E. Soulé, J. Estes, J. Berger, et al., Ecological effectiveness: Conservation goals for interactive species, Conserv. Biol., 17 (2003), 1238–1250.
• 5. L. Oksanen and T. Oksanen, The logic and realism of the hypothesis of exploitation ecosystems, Am. Nat., 118 (2000), 240–261.
• 6. A. M. Springer, J. E. Estes, G. B. van Vliet, et al., Sequential megafaunal collapse in the North Pacific Ocean: An ongoing legacy of industrial whaling?, Proceed. Nat. Aca. Sci., 100 (2003), 12223–12228.
• 7. J. B. C. Jackson, M. X. Kirby, W. H. Berger, et al., Historical over fishing and the recent collapse of coastal ecosystems, Science, 293 (2001), 629–638.
• 8. A. S. Laliberte and W. J. Ripple, Range contractions of North American carnivores and ungulates, BioScience, 54 (2004), 123–138.
• 9. T. H. Tear, J. M. Scott, P. H. Hayward, et al., Recovery plans and the endangered species act:Are criticisms supported by data?, Conserv. Biol., 9 (1995), 182–195.
• 10. D. Jennings, South Florida multi-species recovery plan. vero beach (FL): US fish and wildlife service, (1999).
• 11. I. Nijs and I. Impens, Biological diversity and probability of local extinction of ecosystems, Funct. Ecol., 14 (2000), 46–54.
• 12. C. Borrvall, B. Ebenman and T. Jonsson, Biodiversity lessens the risk of cascading extinction in model food webs, Ecol. Lett., 3 (2000), 131–136.
• 13. Y. Ma and Q. Zhang, Stationary distribution and extinction of a three-species food chain stochastic model, Transact. A. Razmadze Math. Inst., 172 (2018), 251–264.
• 14. J. Baumsteiger and P. B. Moyle, Assessing Extinction, BioScience, 67 (2017), 357–366.
• 15. E. J. Allen, Stochastic differential equations and persistence time for two interacting populations, Dynam. Cont. Discret. Impul. Systems, 5 (1999), 271–281.
• 16. E. J. Allen, L. J. S. Allen and H. Schurz, A comparison of persistence-time estimation for discrete and continuous population models that include demographic and environmental variability, Math. Biosci., 196 (2005), 14–38.
• 17. M. J. Keeling, Multiplicative moments and measures of persistence in ecology, J. Theor. Biol., 205 (2000), 269–281.
• 18. I. Krishnarajah, A. Cook, G. Marion, et al., Novel moment closure approximations in stochastic epidemics, Bullet. Math. Biol., 67 (2005), 855–873.
• 19. R. Lande, S. Engen and B-E. Sæther, Stochastic Population Dynamics in Ecology and Conserva- tion, Oxford University Press, Oxford, 2003.
• 20. Y. Cai, Y. Kang, M. Banerjee, et al., A stochastic SIRS epidemic model with infectious force under intervention strategies, J. Differ. Equat., 259 (2015), 7463–7502.
• 21. Y. Cai, J. Jiao, Z. Gui, et al., Environmental variability in a stochastic epidemic model, Appl. Math. Comput., 329 (2018), 210–226.
• 22. W. Guo, Y. Cai, Q. Zhang, et al., Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage, Physica A, 492 (2018), 2220–2236.
• 23. B. Yang, Y. Cai, K. Wang, et al., Global threshold dynamics of a stochastic epidemic model incorporating media coverage, Adv. Differ. Equat., 462 (2018).
• 24. N. T. J. Bailey, Element of Stochastic Processes with applications to the natural sciences, Wiley, New York, 1964.
• 25. R. M. May, Stability in randomly fluctuating versus deterministic environments, Am. Nat., 107 (1973), 621–650.
• 26. E. Renshaw, Modelling Biological Populations in Space and Time, Cambridge University Press, Cambridge, 1993.
• 27. E. Renshaw, Stochastic population processes: analysis, approximations, simulations, Oxord University Press, New York, 2011.
• 28. A. J. Lotka, Elements of physical biology, Science Progress in the Twentieth Century (1919-1933), 21 (1926), 341–343.
• 29. V. Volterra, Lecons sur la thorie mathmatique de la lutte pour la vie, Gauthier-Villars, Paris, 1931.
• 30. G. F. Gause, The Struggle for Existence, 1934.
• 31. S. L. Pimm, Food webs, Chapman and Hall, New York, USA, 1982.
• 32. R. T. Paine, Food webs: road maps of interaction or grist for theoretical development?, Ecology, 69 (1988), 1648–1654.
• 33. B. Dennis, Allee effects in stochastic populations, Oikos, 96 (2002), 389–401.
• 34. B. Saha, A. R. Bhowmick, J. Chattopadhyay, et al., On the evidence of an allee effect in herring populations and consequences for population survival: A model-based study, Ecol. Modell., 250 (2013), 72–80.
• 35. S. Karlin and H. M. Taylor, A second course in stochastic process, Oxord University Press, New York, 1981.
• 36. J. H. Matis and T. R. Kiffe, On approximating the moments of the equilibrium distribution of a stochastic logistic model, Biometrics, 52 (1996), 980–991.
• 37. J. H. Matis, T. R. Kiffe and P. R. Parthasarathy, On the cumulants of population size for the stochastic power law logistic model, Theor. Popul. Biol., 53 (1998), 16–29.
• 38. J. H. Matis and T. R. Kiffe, Effects of immigration on some stochastic logistic models: A cumulant truncation analysis, Theor. Popul. Biol., 56 (1999), 139–161.
• 39. I. Nåsell, Extinction and quasi-stationarity in the Verhulst logistic model, J. Theor. Biol., 211 (2001), 11–27.
• 40. I. Nåsell, Moment closure and the stochastic logistic model, Theor. Popul. Biol., 63 (2003), 159–168.
• 41. A. R. Bhowmick, B. Saha, S. Ray, J. Chattopadhyay and S. Bhattacharya, Cooperation in species: Interplay of population regulation and extinction through global population dynamics database, Ecol. modell., 312 (2015), 150–165.
• 42. R. Lande, Risks of population extinction from demographic and environmental stochasticity and random catastrophes, Am. Nat., 142 (2004), 911–927.
• 43. B. Saha, On extended growth model, functional response and related mathematical issues: Il- lustration through experimental, history and simulated data, Ph.D thesis, University of Calcutta, 2015.
• 44. A. Hastings and T. Powell, Chaos in a three species food chain, Am. Nat., 72 (1991), 896–903.
• 45. J. W. Bull and M. Maron, How humans drive speciation as well as extinction, Proc. R. Soc. B, 283 (2016).
• 46. S. L. Pimm, J. L. Gittleman and T. Brooks, The future of biodiversity, Science, 269 (1995), 347–350.
• 47. O. E. Sala, Global biodiversity scenarios for the year 2100, Science, 287 (2000), 1770–1774.
• 48. T. Brooks, J. Tobias and A. Balmford, Deforestation and bird extinctions in the Atlantic forest, Anim. Conserv., 2 (1999), 211–222.
• 49. N. Ocampo-Pe˜ nuela, C. N. Jenkins, V. Vijay, et al., Incorporating explicit geospatial data shows more species at risk of extinction than the current Red List, Sci. Adv., 2 (2016).

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